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We consider the problem of row-column sparse linear quadratic controller (LQC) design. An optimization problem is formulated in which the quadratic performance loss is minimized subject to satisfaction of m+n sparsity constraints to obtain the row-column (r, c)-sparse LQC design where m and n refer to the number of inputs and states, respectively and r/c represent the maximum allowed density level...
In this paper, the rank-constrained matrix feasibility problem is considered, where an unknown positive semidefinite (PSD) matrix is to be found based on a set of linear specifications. First, we consider a scenario for which the number of given linear specifications is at least equal to the dimension of the corresponding space of rank-constrained matrices. Given a nominal symmetric and PSD matrix,...
This paper considers the problem of determining the minimum euclidean distance of a point from a polynomial surface in Rn. It is well known that this problem is in general non-convex. The main purpose of the paper is to investigate to what extent Linear Matrix Inequality (LMI) techniques can be exploited for solving this problem. The first result of the paper shows that a lower bound to the global...
Investigating positivity of polynomials over the complex unit disc is a relevant problem in electrical and computer engineering. This paper provides two sufficient and necessary conditions for solving this problem via linear matrix inequalities (LMIs). These conditions are obtained by exploiting trigonometric transformations, a key tool for the representation of polynomials, and results from the theory...
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